US7813904B2ExpiredUtilityA1
Method, apparatus, and computer readable medium based program for simulating an alternate current electric motor using a motor model
Est. expiryNov 17, 2024(expired)· nominal 20-yr term from priority
H02P 23/0077G06F 30/20H02P 23/14G06F 2119/06
25
PatentIndex Score
1
Cited by
17
References
7
Claims
Abstract
This is to provide a computing method of motor model, a motor simulation method and a motor simulation apparatus in which high-speed real-time simulation is made feasible while saving computer resources. A motor model is formulated, motor model which uses a motor model of alternate-current motor which virtually includes the inverse matrix of an inductance matrix L(θ), which is a predetermined function whose variable is a rotary angle θ, and, in the computation of this motor model, the value, which is obtained by computing a matrix λ(θ) which is equal to the inverse matrix of the inductance matrix L(θ), is used as the value of the inverse matrix of the inductance matrix L(θ).
Claims
exact text as granted — not AI-modified1. A computer implemented method of modeling control of an electric motor using a model of a motor, the method using a motor model which is defined by an equation on a stationary coordinate system, the stationary coordinate system specifying a state of an alternate-current motor which comprises a rotor for generating a magnetic-field flux φr and a stator with multiple-phase armature coils wound therearound, said equation including at least a multiple-phase armature current i and a multiple-phase armature voltage U as variables thereof, and the method comprising the steps of:
formulating, utilizing the computer, a motor model in which the inverse matrix of an inductance matrix L(θ), which is a predetermined function whose variable is a rotary angle θ, is converted into a matrix λ(θ), which is a function whose variable is the rotary angle θ; and
computing, utilizing the computer, the matrix λ(θ) to compute the value of the inverse matrix of the inductance matrix L(θ), and feeding the value of the inverse matrix into the equation, which makes said motor model, thereby obtaining resultant values,
wherein the inductance matrix L(θ) is a matrix of inductances of multiple-phase armature coils, the inductances specifying a relationship between a current magnetic flux φs, which is an armature-coil flux linkage resulting from the multiple-phase armature current i, and the multiple-phase armature current i, and
wherein the inverse matrix of the inductance matrix L(θ) is computed by means of computing said matrix λ(θ) based on a d-axis inductance Ld of said alternate-current motor, a q-axis inductance Lq of the alternate-current motor and a leakage inductance Ll thereof.
2. The method according to claim 1 , wherein inductance reciprocal functions λas and λa are computed by feeding the reciprocal λd of the d-axis inductance Ld, the reciprocal λq of the q-axis inductance Lq and the reciprocal λl of the leakage inductance Ll into a Mathematical Formula 37 and a Mathematical Formula 38; and
λ
as
=
1
3
(
λ
q
-
λ
d
)
[
Mathematical
Formula
37
]
λ
a
=
1
3
(
λ
q
+
λ
d
)
-
2
3
λ
ℓ
[
Mathematical
Formula
38
]
λ 11 , λ 12 , λ 13 , λ 21 , λ 22 , λ 23 , λ 31 , λ 32 and λ 33 , the respective elements of the matrix λ(θ), are computed by feeding the computed inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll into a Mathematical Formula 39 through a Mathematical Formula 44
λ 11 =λl+λa−λas cos 2 [Mathematical Formula 39]
λ 12 =−½ λa−λas cos(2θ−⅔π) [Mathematical Formula 40]
λ 13 =−½ λa−λas cos(2θ+⅔π) [Mathematical Formula 41]
λ 22 =λl+λa−λas cos(2θ+⅔π) [Mathematical Formula 42]
λ 23 =−½ λa−λas cos 2θ [Mathematical Formula 43]
λ 33 =λl+λa−λas cos(2θ−⅔π) [Mathematical Formula 44]
λ 21 =λ 12 [Mathematical Formula 45]
λ 31 =λ 13 [Mathematical Formula 46]
λ 32 =λ 23 . [Mathematical Formula 47]
3. A computer implemented method of modeling control of an electric motor using a model of a motor, the method using a motor model which is defined by an equation on a stationary coordinate system, the stationary coordinate system specifying a state of an alternate-current motor which comprises a rotor for generating a magnetic-field flux ψr and a stator with multiple-phase armature coils wound therearound, said equation including at least a multiple-phase armature current i and a multiple-phase armature voltage U as variables thereof, and the computing method being a computing method of motor model computing another values of said variables by feeding numerical values into predetermined variables, the method comprising the step of:
forming, utilizing the computer, the motor model using:
a first equation, which specifies a quantitative relationship between a current magnetic flux ψs, which is an armature-coil flux linkage resulting from the multiple-phase armature current i, a predetermined function whose variable is a rotary angle θ and the multiple-phase armature voltage U, and
a second equation, which specifies a quantitative relationship between the current magnetic flux ψs, said predetermined function and the multiple-phase armature current i,
wherein the current magnetic flux ψs is computed by means of feeding said predetermined function and a value of the multiple-phase armature voltage U into said first equation,
wherein the multiple-phase armature current i is computed by means of feeding the current magnetic flux ψs and a value of said predetermined function into said second equation,
wherein said predetermined function is an inverse matrix of inductance matrix L(θ), which is a predetermined matrix whose variable is the rotary angle θ, and
wherein said inductance matrix L(θ) is a matrix of inductances of the multiple-phase armature coils, the inductances specifying a relationship between the current magnetic flux ψs, which is an armature-coil flux linkage resulting from the multiple-phase armature current i, and the multiple-phase current i,
said inverse matrix is equal to a matrix λ(θ), and
the respective elements of said matrix λ(θ) are functional values of a d-axis inductance Ld of said alternate-current motor, a q-axis inductance Lq of the alternate-current motor and a leakage inductance Ll thereof.
4. A non-transitory computer readable medium having stored thereon a motor-model computing program for computing a motor model, the motor model being defined by an equation on a stationary coordinate system, the stationary coordinate system specifying a state of an alternate-current motor which comprises a rotor for generating a magnetic-field flux ψr and a stator with multiple-phase armature coils wound therearound, said equation including at least a multiple-phase armature current i and a multiple-phase armature voltage U as variables thereof, the motor-model computing program comprising the steps of:
computing a matrix λ(θ), being constituted of a function whose variable is a rotary angle θ, and additionally being a function which is equal to the inverse matrix of an inductance matrix L(θ) which specifies a relationship between a current magnetic flux ψs, which is an armature-coil flux linkage resulting from the multiple-phase armature current i, and the multiple-phase armature current i; and
obtaining resultant values of said equation by feeding the value of said matrix λ(θ) into the equation as the value of the inverse matrix of the inductance matrix L(θ), which is included in said equation,
wherein the step of computing said matrix λ(θ) comprises the steps of:
computing inductance reciprocal functions λas and λa by feeding the reciprocal λd of d-axis inductance Ld of said alternate-current motor, the reciprocal λq of q-axis inductance Lq thereof and the reciprocal λl of leakage inductance Ll thereof into a Mathematical Formula 37 and a Mathematical Formula 38, and
λ
as
=
1
3
(
λ
q
-
λ
d
)
[
Mathematical
Formula
37
]
λ
a
=
1
3
(
λ
q
+
λ
d
)
-
2
3
λ
ℓ
[
Mathematical
Formula
38
]
computing λ 11 , λ 12 , λ 13 , λ 21 , λ 22 , λ 23 , λ 31 , λ 32 and λ 33 , the respective elements of the matrix λ(θ), by feeding the computed inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll into a Mathematical Formula 39 through a Mathematical Formula 44
λ 11 =λl+λa−λas cos 2 [Mathematical Formula 39]
λ 12 =−½ λa−λas cos(2θ−⅔π) [Mathematical Formula 40]
λ 13 =−½ λa−λas cos(2θ+⅔π) [Mathematical Formula 41]
λ 22 =λl+λa−λas cos(2θ+⅔π) [Mathematical Formula 42]
λ 23 =−½ λa−λas cos 2θ [Mathematical Formula 43]
λ 33 =λl+λa−λas cos(2θ−⅔π) [Mathematical Formula 44]
λ 21 =λ 12 [Mathematical Formula 45]
λ 31 =λ 13 [Mathematical Formula 46]
λ 32 =λ 23 . [Mathematical Formula 47]
5. A non-transitory computer readable medium having stored thereon a motor-model computing program that when executed by a computer causes the computer to perform a motor-model method for computing a motor model, the motor model being defined by an equation on a stationary coordinate system, the stationary coordinate system specifying a state of an alternate-current motor which comprises a rotor for generating a magnetic-field flux ψr and a stator with multiple-phase armature coils wound therearound, said equation including at least a multiple-phase armature current i and a multiple-phase armature voltage U as variables thereof, the motor-model method comprising the steps of:
computing a current magnetic flux ψs, which is an armature-coil flux linkage resulting from the multiple-phase armature current i, by means of feeding a predetermined function, whose variable is a rotary angle θ, and a value of the multiple-phase armature voltage U into a first equation, which specifies a quantitative relationship between the current magnetic flux ψs, said predetermined function and the multiple-phase armature voltage U; and
computing the multiple-phase armature current i by means of feeding the current magnetic flux ψs and a value of said predetermined function into a second equation, which specifies a quantitative relationship between the current magnetic flux ψs, said predetermined function and the multiple-phase armature current i,
wherein said step of computing the current magnetic flux ψs comprises the steps of:
computing a matrix λ(θ), which is a function being equal to the inverse matrix of an inductance matrix L(θ) specifying a relationship between the current magnetic flux ψs and the multiple-phase armature current i, and
obtaining a resultant value for said equation by feeding the value of said matrix λ(θ) into the equation as the value of the inverse matrix of the inductance matrix L(θ), which is included in said equation,
wherein said step of computing the matrix λ(θ) comprises the steps of:
computing inductance reciprocal functions λas and λa by feeding the reciprocal λl of d-axis inductance Ld of said alternate-current motor, the reciprocal λq of q-axis inductance Lq thereof and the reciprocal λl of leakage inductance Ll thereof into a Mathematical Formula 37 and a Mathematical Formula 38, and
λ
as
=
1
3
(
λ
q
-
λ
d
)
[
Mathematical
Formula
37
]
λ
a
=
1
3
(
λ
q
+
λ
d
)
-
2
3
λ
ℓ
[
Mathematical
Formula
38
]
computing λ 11 , λ 12 , λ 13 , λ 21 , λ 22 , λ 23 , λ 31 , λ 32 and λ 33 , the respective elements of the matrix λ(θ), by feeding the computed inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll into a Mathematical Formula 39 through a Mathematical Formula 44
λ 11 =λl+λa−λas cos 2 [Mathematical Formula 39]
λ 12 =−½ λa−λas cos(2θ−⅔π) [Mathematical Formula 40]
λ 13 =−½ λa−λas cos(2θ+⅔π) [Mathematical Formula 41]
λ 22 =λl+λa−λas cos(2θ+⅔π) [Mathematical Formula 42]
λ 23 =−½ λa−λas cos 2θ [Mathematical Formula 43]
λ 33 =λl+λa−λas cos(2θ−⅔π) [Mathematical Formula 44]
λ 21 =λ 12 [Mathematical Formula 45]
λ 31 =λ 13 [Mathematical Formula 46]
λ 32 =λ 23 . [Mathematical Formula 47]
6. A computer implemented simulation method of periodically executing a computing step of computing a state of an object model for imitating an operation of a predetermined object, the objective model being defined by an equation which includes the inverse matrix of a predetermined matrix L(θ) being a function changing periodically, thereby simulating the state of said objective model in real time, the state being defined by said objective model, the simulation method comprising the step of:
defining, using the computer, a matrix λ(θ), which is a function being equal to said inverse matrix, and computing the respective elements of said matrix λ(θ), thereby performing the computation of the inverse matrix of said matrix L(θ),
wherein said objective model is a motor model which is defined by an equation on a stationary coordinate system, the stationary coordinate system specifying a state of an alternate-current motor which comprises a rotor for generating a magnetic-field flux ψr and a stator with multiple-phase armature coils wound therearound, said equation including at least a multiple-phase armature current i and a multiple-phase armature voltage U as variables thereof and
said matrix L(θ) is a matrix of inductances of multiple-phase armature coils, inductances whose variable is a rotary angle θ and which specify a relationship between a current magnetic flux ψs, which is an armature-coil flux linkage resulting from the multiple-phase armature current i, and the multiple-phase current i,
wherein said matrix λ(θ) is computed based on a d-axis inductance Ld of said alternate-current motor, a q-axis inductance Lq of the alternate-current motor and a leakage inductance Ll thereof.
7. The computer implemented simulation method according to claim 6 , wherein inductance reciprocal functions λas and λa are computed by feeding the reciprocal λd of the d-axis inductance Ld, the reciprocal λq of the q-axis inductance Lq and the reciprocal λl of the leakage inductance Ll into a Mathematical Formula 37 and a Mathematical Formula 38, and
λ
as
=
1
3
(
λ
q
-
λ
d
)
[
Mathematical
Formula
37
]
λ
a
=
1
3
(
λ
q
+
λ
d
)
-
2
3
λ
ℓ
[
Mathematical
Formula
38
]
λ 11 , λ 12 , λ 13 , λ 21 , λ 22 , λ 23 , λ 31 , λ 32 and λ 33 , the respective elements of the matrix λ(θ), are computed by feeding the computed inductance reciprocal functions λas and λa and the reciprocal λl of the leakage inductance Ll into a Mathematical Formula 39 through a Mathematical Formula 44
λ 11 =λl+λa−λas cos 2 [Mathematical Formula 39]
λ 12 =−½ λa−λas cos(2θ−⅔π) [Mathematical Formula 40]
λ 13 =−½ λa−λas cos(2θ+⅔π) [Mathematical Formula 41]
λ 22 =λl+λa−λas cos(2θ+⅔π) [Mathematical Formula 42]
λ 23 =−½ λa−λas cos 2θ [Mathematical Formula 43]
λ 33 =λl+λa−λas cos(2θ−⅔π) [Mathematical Formula 44]
λ 21 =λ 12 [Mathematical Formula 45]
λ 31 =λ 13 [Mathematical Formula 46]
λ 32 =λ 23 . [Mathematical Formula 47]Cited by (0)
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